Variance Reduced Training with Stratified Sampling for Forecasting Models

TL;DR

This paper introduces SCott, a stratified sampling-based variance reduction method for training forecasting models more efficiently, especially under heterogeneous time series data, with proven convergence and empirical faster convergence.

Contribution

It proposes SCott, a novel variance-reduced optimizer using stratified sampling with control variates, and provides theoretical convergence guarantees for non-convex objectives.

Findings

SCott converges faster than baseline optimizers in experiments.

Stratified sampling reduces gradient variance in heterogeneous data.

Theoretical convergence guarantee for SCott on smooth non-convex functions.

Abstract

In large-scale time series forecasting, one often encounters the situation where the temporal patterns of time series, while drifting over time, differ from one another in the same dataset. In this paper, we provably show under such heterogeneity, training a forecasting model with commonly used stochastic optimizers (e.g. SGD) potentially suffers large variance on gradient estimation, and thus incurs long-time training. We show that this issue can be efficiently alleviated via stratification, which allows the optimizer to sample from pre-grouped time series strata. For better trading-off gradient variance and computation complexity, we further propose SCott (Stochastic Stratified Control Variate Gradient Descent), a variance reduced SGD-style optimizer that utilizes stratified sampling via control variate. In theory, we provide the convergence guarantee of SCott on smooth non-convex objectives. Empirically, we evaluate SCott and other baseline optimizers on both synthetic and real-world time series forecasting problems, and demonstrate SCott converges faster with respect to both iterations and wall clock time.